On status of Boltzmann kinetic theory in the framework of statistical mechanics

TL;DR

This paper critically examines the derivation of the Boltzmann kinetic equation from BBGKY equations, highlighting the irreversibility introduced in earlier derivations and proposing an alternative approach that preserves reversibility.

Contribution

It demonstrates that previous derivations incorrectly assume irreversibility and introduces a new method that maintains reversibility, clarifying conditions for deriving the Boltzmann equation.

Findings

Previous derivations are fundamentally flawed due to irreversibility assumptions.

The Boltzmann equation can only be derived from BBGKY equations in spatially uniform gases.

An alternative approach preserves reversibility and clarifies the conditions for reduction.

Abstract

It is shown that early suggested derivation of the Boltzmann kinetic equation for dilute hard sphere gas from the time-reversible BBGKY equations is incorrect since in fact a priori substitutes for them definite irreversible equations. Alternative approach to analysis of the hard sphere gas is formulated which conserves the reversibility and makes it clear that at any gas density one can reduce the BBGKY equations to the Boltzmann equation only in case of spatially uniform gas.